"If you don't know what work may help that person, would you ask directly how you may provide a benefit to him/her?"
No I wouldn't. I get these sort of emails myself,though I am just a programmer and have no world class expertise even in programming, and I know what timewasters they can be.
More importantly I let my work lead to potential mentors than the other way round. In other words, I'll work on what interests me/I think is important even if no mentors are available. Mentors are an occasional aid, not a dependency, to doing good work. Which leads me to
(b) The desire to take the "optimal path" (no such thing exists for most realworld situations) can in itself be a paralyzing factor. Taking some paths, realizing they are not right for you and then backtracking is part of the learning process. This time is not "wasted". Seeing it thus only shows you are at a certain stage in learning how to learn, and need to move a little further.
Doing this exploration and backtracking improves your skill in choosing and walking paths. Sure, too much of it can be debilitating, but knowing when to stop and when to continue is itself a valuable skill, which can be acquired only by gaining experience and reflecting on it, not by someone else trying to guess the 'right path' for you.
If you completely avoid these situations, waiting for someone else to give you an "optimal" path, you end up (in the best case) as someone who can take a path only when someone else lays out all the pros and cons of each path. And that is not a good place to be, even if such a situation were possible (which is usually not the case, though in some highly structured environments like studying for an academic degree, it might be possible)